Question: Stephanie is 2 times as old as Ashley. Fifteen years ago, Stephanie was 5 times as old as Ashley. How old is Stephanie now?
Solution: We can use the given information to write down two equations that describe the ages of Stephanie and Ashley. Let Stephanie's current age be $s$ and Ashley's current age be $a$ The information in the first sentence can be expressed in the following equation: $s = 2a$ Fifteen years ago, Stephanie was $s - 15$ years old, and Ashley was $a - 15$ years old. The information in the second sentence can be expressed in the following equation: $s - 15 = 5(a - 15)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $s$ , it might be easiest to solve our first equation for $a$ and substitute it into our second equation. Solving our first equation for $a$ , we get: $a = s / 2$ . Substituting this into our second equation, we get: $s - 15 = 5($ $(s / 2)$ $- 15)$ which combines the information about $s$ from both of our original equations. Simplifying the right side of this equation, we get: $s - 15 = \dfrac{5}{2} s - 75$ Solving for $s$ , we get: $\dfrac{3}{2} s = 60$ $s = \dfrac{2}{3} \cdot 60 = 40$.